A blown MAIN fuse and BLACK finding continuity to ground tells me yuor Black wire within the harness has shorted out. This wire also serves the RH bar controls for KILL, becomes BLK/WHT to coils with RUN. Since you had the issue, then no spark, that would lead me to investigate the KILL switch wiring and the coil wire (power side).
It is not unusual for a wire to fray behind the headlight and underneath the bars. If the Black does, it’s giong to short out promptly. With that wire damaged, the Reg/Rec functions will be totally askew.
With the Black disconnected from Reg, do you get continuity to ground anywhere on the bike? To the battery NEG, motor bolts, frame screw? Also, with the key OFF, test this with RUN set to on.